Being online all the time? Who cares, I am anyway. I literally couldn't care less about that.
my point of view on this:
-I don't care at all about internet activation periodic check (such as once per week, or once per game update as Mass Effect is)
-I care a little bit but nothing major if the internet check is "once every game startup" : my internet is a bit slow (1024/128kbit and shared)
so it might very well add a couple of seconds on the startup of the game...
-I am kind of annoyed if the internet check is permanent : my internet has its downtimes here and there and it's annoying as hell already without having a game throw you out of it while running ...
and of course the servers WILL have down times, never ever saw a server with more than 99% up time even google had its share of issues even though they have truly massive clusters of servers...
also don't know about other countries, but in France, ADSL coverage is NOT 100% so that means there's still people with limited pay-per-time internet connections out there, depending on where they live ...
(not going into security & privacy issues since these were discussed before already)
edit: thought of something else: imagine the following situation
someone is playing it, but having some difficulties getting through a specific stage, he gets killed & restart about 9 times
then on the 10th times he's about to finish when *poof* no internet connection... how annoying is that ?
Also how will cutscenes be handled ? will it cut you off in the middle of it ? will it allow you to resume where you were in the middle of it ? or will it allow you to restart the whole cutscene ? or will it save the game before exiting as if you had finished viewing it therefore preventing you from watching it again ?